Fluency in math facts and procedures is critical for math achievement overall and often challenging for students with emotional and behavioral disorders to develop. This article describes how to implement two complementary and evidence-based practice strategies, incremental rehearsal and Cover-Copy-Compare, to build declarative and procedural fluency in tandem. How-to steps, example materials, and additional resources are provided.
BaroodyA. J. (2011). Learning: A framework. In FennellF. (Ed.), Achieving fluency: Special education and mathematics (pp. 15–58). National Council of Teachers of Mathematics.
2.
BeckM.BurnsM. K.LauM. (2009). The effect of preteaching reading skills on the on-task behavior of children identified with behavioral disorders. Behavioral Disorders, 34, 91–99.
3.
BeckerA.McLaughlinT.WeberK. P.GowerJ. (2009). The effects of cover, copy, and compare without additional error drill on multiplication fact fluency and accuracy. Electronic Journal of Research in Educational Psychology, 15, 747–760.
4.
BinderC. (2003). Doesn’t everybody need fluency?Performance Improvement, 42, 14–20.
5.
BlackorbyJ.ChorostM.GarzaN.GuzmanA. (2003). The academic performance of secondary students with disabilities. In WagnerM.MarderC.BlackorbyJ.CametoR.NewmanL.LevineP.Davies-MercierE. (Eds.), The achievements of youth with disabilities during secondary school. A report from the National Longitudinal Transition Study-2 (pp. 4-1–4-22). SRI International.
6.
BlackorbyJ.ChorostM.GarzaN.GuzmanA. (2005). The academic performance of elementary and middle school students with disabilities. In BlackorbyJ.WagnerM.CametoR.DaviesE.LevineP.NewmanL.MarderC.SumiC. (with ChorostM.GarzaN.GuzmanA.) (Eds.), Engagement, academics, social adjustment, and independence: The achievements of elementary and middle school students with disabilities. A report from the Special Education Elementary Longitudinal Study (pp. 4-1–4-14). SRI International.
7.
BoothJ. L.CooperL. A.DonovanM. S.HuygheA.KoedingerK. R.Paré-BlagoevE. J. (2015). Design-based research within the constraints of practice: AlgebraByExample. Journal of Education for Students Placed at Risk, 20, 79–100.
8.
BruhnA.McDanielS.KreighC. (2015). Self-monitoring interventions for students with behavior problems: A systematic review of current research. Behavioral Disorders, 40, 102–121. https://doi.org/10.17988/BD-13-45.1
9.
BurnsM. K. (2005). Using incremental rehearsal to increase fluency of single-digit multiplication facts with children identified as learning disabled in mathematics computation. Education and Treatment of Children, 28, 237–249.
10.
BurnsM. K.AguilarL. N.YoungH.PreastJ. L.TaylorC. N.WalshA. D. (2019). Comparing the effects of incremental rehearsal and traditional drill on retention of mathematics facts and predicting the effects with memory. School Psychology, 34, 521–530. https://doi.org/10.1037/spq0000312
11.
BurnsM. K.VanDerHeydenA. M.BoiceC. H. (2008). Best practices in intensive academic interventions. Best Practices in School Psychology, 4, 1151–1162.
12.
ByrnesJ. P.WasikB. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777–786.
13.
CancioE. J.WestR. P.YoungK. R. (2004). Improving mathematics homework completion and accuracy of students with EBD through self-management and parent participation. Journal of Emotional and Behavioral Disorders, 12, 9–22. https://doi.org/10.1177/10634266040120010201
14.
CarrollW. M. (1994). Using worked examples as an instructional support in the algebra classroom. Journal of Educational Psychology, 86, 360–367.
15.
ClarkR. C.NguyenF.SwellerJ. (2011). Efficiency in learning to manage cognitive load. Wiley.
16.
CoddingR. S.BurnsM. K.LukitoG. (2011). Meta-analysis of mathematic basic-fact fluency interventions: A component analysis. Learning Disabilities Research & Practice, 26, 36–47. https://doi.org/10.1111/j.1540-5826.2010.00323.x
17.
DalyE. J.III.MartensB. K.BarnettD.WittJ. C.OlsonS. C. (2007). Varying intervention delivery in response to intervention: Confronting and resolving challenges with measurement, instruction, and intensity. School Psychology Review, 36, 562–581.
18.
De MeyerH.BeckersT.TrippG.van der OordS. (2019). Reinforcement contingency learning in children with ADHD: Back to the basics of behavior therapy. Journal of Abnormal Child Psychology, 47, 1889–1902.
19.
EnnisR. P.EvanovichL.LosinskiM.JolivetteK.KimballK. (2017). Behavioral, academic, and social characteristics of students with EBD served in a residential facility. In CookB. G.TankersleyM.LandrumT. J. (Eds.), Advances in learning and behavioral disabilities (Vol. 30, pp. 93–111). Emerald Insight.
20.
GearyD. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345–362.
GearyD. C.WidamanK. F. (1992). Numerical cognition: On the convergence of componential and psychometric models. Intelligence, 16, 47–80.
23.
GrafmanJ. M.CatesG. L. (2010). The differential effects of two self-managed math instruction procedures: Cover, Copy, Compare versus Copy, Cover, and Compare. Psychology in the Schools, 47, 153–165. https://doi.org/10.1002/pits.20459
24.
HansenC. L. (1978). Writing skills. In HaringN. G.LovittT. C.EatonM. D.HansenC. L. (Eds.), The fourth R: Research in the classroom (pp. 93–126). Merrill.
25.
HansenN.JordanN. C.FernandezE.SieglerR. S.FuchsL.GerstenR.MicklosD. (2015). General and math-specific predictors of sixth-graders’ knowledge of fractions. Cognitive Development, 35, 34–49. https://doi.org/10.1016/j.cogdev.2015.02.001
26.
HodgeJ.RiccominiP. J.BufordR.HerbstM. H. (2006). A review of instructional interventions in mathematics for students with emotional and behavioral disorders. Behavioral Disorders, 31(3), 297–311. https://doi.org/10.1177/019874290603100304
27.
HowardM. W.KahanaM. J. (2002). A distributed representation of temporal context. Journal of Mathematical Psychology, 46, 269–299.
28.
JordanN. C.MontaniT. O. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30, 624–634. https://doi.org/10.1177/002221949703000606
29.
KlingbeilD. A.MoeyaertM.ArcherC. T. (2017). Efficacy of peer-mediated incremental rehearsal for English language learners. School Psychology Review, 46, 122–140. https://doi.org/10.1080/02796015.2017.12087605
30.
MacQuarrieL. L.TuckerJ. A.BurnsM. K.HartmanB. (2002). Comparison of retention rates using traditional, drill sandwich, and incremental rehearsal flash card methods. School Psychology Review, 31, 584–595. https://doi.org/10.1080/02796015.2002.12086176
31.
MattisonR. E.HooperS. R.CarlsonG. A. (2006). Neuropsychological characteristics of special education students with serious emotional/behavioral disorders. Behavioral Disorders, 31, 176–188.
32.
McGuiganC. A. (1975). The add-a-word spelling program. Experimental Education Unit (Working Paper No. 53). University of Washington.
33.
McVancelS. M.MissallK. N.BruhnA. L. (2018). Examining incremental rehearsal: Multiplication fluency with fifth-grade students with math IEP goals. Contemporary School Psychology, 22, 220–232. https://doi.org/10.1007/s40688-018-0178-x
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. US Department of Education.
36.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Mathematics Learning Study Committee.
37.
NelsonJ. R.BennerG. J.LaneK.SmithB. W. (2004). Academic achievement of K-12 students with emotional and behavioral disorders. Exceptional Children, 71, 59–73. https://doi.org/10.1177/001440290407100104
38.
PassolunghiM. C.CostaH. M. (2019). Working memory and mathematical learning. In FritzA.HaaseV. G.RäsänenP. (Eds.), International handbook of mathematical learning difficulties: From the laboratory to the classroom (pp. 407–421). Springer. https://doi.org/10.1007/978-3-319-97148-3_25
39.
Petersen-BrownS.BurnsM. (2011). Adding a vocabulary component to incremental rehearsal to enhance retention and generalization. School Psychology Quarterly, 26, 245–255. https://doi.org/10.1037/a0024914
40.
PhippsL.RobinsonE. L.GrebeS. (2020). An evaluation of strategic incremental rehearsal on sight word acquisition among students with SLD in reading. Journal of Behavioral Education. Advance online publication. https://doi.org/10.1007/s10864-020-09398-y
41.
PoncyB. C.DuhonG. J.LeeS. B.KeyA. (2010). Evaluation of techniques to promote generalization with basic math fact skills. Journal of Behavioral Education, 19, 76–92. https://doi.org/10.1007/s10864-010-9101-x
42.
PoncyB. C.SkinnerC. H.AxtellP. K. (2010). An investigation of detect, practice, and repair to remedy math-fact deficits in a group of third-grade students. Psychology in the Schools, 47, 342–353. https://doi.org/10.1002/pits.20474
43.
PoncyB. C.SkinnerC. H.JaspersK. E. (2007). Evaluating and comparing interventions designed to enhance math fact accuracy and fluency: Cover, copy, and compare versus taped problems. Journal of Behavioral Education, 16, 27–37.
44.
PophamM.CountsJ.RyanJ. B.KatsiyannisA. (2018). A systematic review of self-regulation strategies to improve academic outcomes of students with EBD. Journal of Research in Special Educational Needs, 18, 239–253. https://doi.org/10.1111/1471-3802.12408
45.
RyanJ. B.ReidR.EpsteinM. H. (2004). Peer-mediated intervention studies on academic achievement for students with EBD: A review. Remedial and Special Education, 25(6), 330–341. https://doi.org/10.1177/07419325040250060101
46.
SchraubenK. S.DeanA. J. (2019). Cover-Copy-Compare for multiplication with students with emotional and behavioral disorders: A brief report. Behavioral Disorders, 45, 22–28. https://doi.org/10.1177/0198742918808484
47.
SkinnerC. H.BambergH. W.SmithE. S.PowellS. S. (1993). Cognitive cover, copy, and compare: Subvocal responding to increase rates of accurate division responding. Remedial and Special Education, 14, 49–56. https://doi.org/10.1177/074193259301400107
48.
SkinnerC. H.FordJ. M.YunkerB. D. (1991). A comparison of instructional response requirements on the multiplication performance of behaviorally disordered students. Behavioral Disorders, 17, 56–65. https://doi.org/10.1177/019874299101700107
49.
SutherlandK. S.AlderN.GunterP. L. (2003). The effect of varying rates of opportunities to respond to academic requests on the classroom behavior of students with EBD. Journal of Emotional and Behavioral Disorders, 11, 239–248. https://doi.org/10.1177/10634266030110040501
VolpeR. J.BurnsM. K.DuBoisM.ZaslofskyA. F. (2011). Computer-assisted tutoring: Teaching letter sounds to kindergarten students using incremental rehearsal. Psychology in the Schools, 48, 332–342. https://doi.org/10.1002/pits.20557
52.
WeiX.LenzK. B.BlackorbyJ. (2013). Math growth trajectories of students with disabilities: Disability category, gender, racial, and socioeconomic status differences from ages 7 to 17. Remedial and Special Education, 34, 154–165. https://doi.org/10.1177/0741932512448253
53.
WitzelB. S.RiccominiP. J. (2007). Optimizing math curriculum to meet the learning needs of students. Preventing School Failure, 52, 13–18.
54.
ZamarianL.López-RolónA.DelazerM. (2007). Neuropsychological case studies on arithmetic processing. In BerchD. B.MazzoccoM. M. M. (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 245–263). Paul H. Brookes.
